Author:  Kevin P. Knudson
Title:  Relative completions of linear groups over <b>Z</b>[t] and
<b>Z</b>[t,t<sup>-1</sup>]

<p>In this paper we compute the completion of the groups 
SL<sub>n</sub>(<b>Z</b>[t]) and SL<sub>n</sub>(<b>Z</b>[t,t<sup>-1</sup>])
with respect to the obvious homomorphisms to SL<sub>n</sub>(<b>Q</b>); this
is a generalization of the classical Malcev completion (which is trivial
for these groups).  It turns out that the obvious guess is the correct one,
namely the proalgebraic group SL<sub>n</sub>(<b>Q</b>[[T]]).  We use this
result to study the rational second cohomology of the groups
SL<sub>n</sub>(R) for R=<b>Z</b>[t], <b>Z</b>[t,t<sup>-1</sup>].</p>